Probably an old topic now, but :
Laker were tied to Lord Brothers (Gatwick) and Arrowsmith (Liverpool/Manchester).
Britannia were tied to the four operators that came together to form Thomson, namely Universal Sky Tours, Gaytours, Luxitours and Riviera. Britannia also operated extensive programmes for Horizon Midlands out of Birmingham, which somehow was detached from the main Horizon company and was a significant competitor to those other Thomson brands.
Monarch were tied to Cosmos, although they long operated for them just out of Luton, and Cosmos used Dan-Air from elsewhere.
Court Line were tied to Clarksons, although they also only operated for them from Luton and Bristol/Cardiff. Clarksons also had extensive operations out of Gatwick, Manchester and Teesside (their North-East departure point) which they used Dan-Air for.
British Eagle operated extensively for Lunn Poly from Heathrow (the last significant holiday charter operation from there) until they went out of business at the end of 1968, when Lunns had to move over to Dan-Air, surprisingly out of Luton.
Caledonian (the original one) were tied with Global Holidays.
Britsh United were used by both Horizon and Lyons for some time; Lyons later left them and went to Channel Airways, where they were the principal users of that airline's dilapadated Comet fleet at the end of its existence.
BEA Airtours made a big arrival at the end of the 1960s with Enterprise (mass market) and Sovereign (upmarket).
Dan-Air had a different sales model and wasn't connected with anyone in particular, but ended up operating for just about all of them, along with very many smaller operators.
These carriers did of course operate for others (especially out of Gatwick), and there was sharing of capacity from secondary points.